Related papers: The type III manufactory
We study the two-sided Guionnet-Jones-Shlyakhtenko construction applied to the group planar algebra $P(\mathcal{G})$ of a finite non-trivial group $\mathcal{G}$. This produces a sequence of von Neumann algebras $M^k$ for $k \geq 0$ with no…
The Riemann hypothesis is, and will hopefully remain for a long time, a great motivation to uncover and explore new parts of the mathematical world. After reviewing its impact on the development of algebraic geometry we discuss three…
A novel invariant decomposition of diagonalizable $n \times n$ matrices into $n$ commuting matrices is presented. This decomposition is subsequently used to split the fundamental representation of $\mathfrak{su}(3)$ Lie algebra elements…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
In this paper we analyze the structure of some sets of non-commutative moments of elements in a finite von Neumann algebra M. If the fundamental group of M is R_+\{0}, then the moment sets are convex, and if M is isomorphic to M tensor M,…
We study a three-player variation of the impartial avoidance game introduced by Anderson and Harary. Three players take turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an element…
Given a finitely generated free monoid $X$ and a morphism $\phi : X\to X$, we show that one can construct an algebra, which we call an iterative algebra, in a natural way. We show that many ring theoretic properties of iterative algebras…
We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…
Let $X$ be a finite connected graph, each of whose vertices has degree at least three. The fundamental group $\Gamma$ of $X$ is a free group and acts on the universal covering tree $\Delta$ and on its boundary $\partial \Delta$, endowed…
We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and…
We study several model-theoretic aspects of W$^*$-probability spaces, that is, $\sigma$-finite von Neumann algebras equipped with a faithful normal state. We first study the existentially closed W$^*$-spaces and prove several structural…
We consider a class of infinite-dimensional, modular, graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series. We identify two subclasses of Nottingham Lie…
An example is given of a simple, unital C*-algebra which contains an infinite and a non-zero finite projection. This C*-algebra is also an example of an infinite simple C*-algebra which is not purely infinite. A corner of this C*-algebra is…
We discuss the algebra of $N\times N$ matrices as a reduced quantum plane. A $3-$nilpotent deformed differential calculus involving a complex parameter $q$ is constructed. The two cases, $q$ $3^{rd}$ and $N^{th}$ root of unity are…
Tiling spaces are constructed using a metric in which two tilings of $\mathbb{R}^n$ are close if and only if, after a small translation, they agree on a large ball around the origin. We construct analogous spaces to study random…
We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…
Gravity equations are often used to evaluate the effects of trade policies, such as regional trade agreements. We argue that their suitability for this purpose critically depends on their ability to produce unbiased out-of-sample…
We study several notions of ultraproducts of von Neumann algebras from a unifying viewpoint. In particular, we show that for a sigma-finite von Neumann algebra $M$, the ultraproduct $M^{\omega}$ introduced by Ocneanu is a corner of the…
Using a m\'elange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably…
We prove some unique prime factorization results for tensor products of type $II_1$ factors of the form $\Gamma_q(\mathbb{C}, S \otimes H)$ arising from symmetric independent copies with sub-exponential dimensions of the spaces $D_k(S)$ and…